docs: def flow_meter_discharge(D, Do, P1, P2, rho, C, expansibility=1.0):
      r'''Calculates the flow rate of an orifice plate based on the geometry
      of the plate, measured pressures of the orifice, and the density of the
      fluid.
      
      .. math::
          m = \left(\frac{\pi D_o^2}{4}\right) C \frac{\sqrt{2\Delta P \rho_1}}
          {\sqrt{1 - \beta^4}}\cdot \epsilon
          
      Parameters
      ----------
      D : float
          Upstream internal pipe diameter, [m]
      Do : float
          Diameter of orifice at flow conditions, [m]
      P1 : float
          Static pressure of fluid upstream of orifice at the cross-section of
          the pressure tap, [Pa]
      P2 : float
          Static pressure of fluid downstream of orifice at the cross-section of
          the pressure tap, [Pa]
      rho : float
          Density of fluid at `P1`, [kg/m^3]
      C : float
          Coefficient of discharge of the orifice, [-]
      expansibility : float, optional
          Expansibility factor (1 for incompressible fluids, less than 1 for
          real fluids), [-]
  
      Returns
      -------
      m : float
          Mass flow rate of fluid, [kg/s]
  
      Notes
      -----
      This is formula 1-12 in [1]_ and also [2]_.
  
      Examples
      --------
      >>> flow_meter_discharge(D=0.0739, Do=0.0222, P1=1E5, P2=9.9E4, rho=1.1646, 
      ... C=0.5988, expansibility=0.9975)
      0.01120390943807026
  
      References
      ----------
      .. [1] American Society of Mechanical Engineers. Mfc-3M-2004 Measurement 
         Of Fluid Flow In Pipes Using Orifice, Nozzle, And Venturi. ASME, 2001.
      .. [2] ISO 5167-2:2003 - Measurement of Fluid Flow by Means of Pressure 
         Differential Devices Inserted in Circular Cross-Section Conduits Running
         Full -- Part 2: Orifice Plates.
      '''
      beta = Do/D
      beta2 = beta*beta
      return (0.25*pi*Do*Do)*C*expansibility*(
              (2.0*rho*(P1 - P2))/(1.0 - beta2*beta2))**0.5